# Hubble's Law conundrum

1. Jan 16, 2012

### ch@rlatan

Imagine this;-

Two planets and a star separated by cosmological distances that share an amost linear positional relationship - the star is not in the middle and both planets have a direct eyeline to it. Both planets have intelligent life and both are observing the star's redshift.
Two photons leave the star's surface from almost the same place and at almost the same time (relative to each other). Each of the planets receives one of the photons and notes the redshift.
Hubble's Law requires that the planet further away should note a greater redshift.
How is it that the photons contain different information for different observers?

2. Jan 16, 2012

### Chronos

The planets are not equidistant from the star in question.

3. Jan 16, 2012

### ch@rlatan

Sure, this is a condition for the question.

The crux is this. When the photons were emitted they had the same information, they were emitted under the same conditions - the Doppler effect is the stretching (or compression) of the photon at the time of emission. Once free of the emitter's (sun's) gravitational influence the photons can no longer gain information from their source and are just travelling as you would expect light to travel. But to satisfy Hubble's Law they must still arrive at their respective destinations with different information. Begging the question;- Did the information change en-route?

4. Jan 16, 2012

### marcus

You confuse the cosmological redshift with a Doppler effect "at the time of emission"

This is a common mistake. The redshift is not a simple Doppler effect depending merely on relative velocities at time of emission and or time of reception.

The usual way one calculates the redshift uses to ratio of distance now (at reception) to distance then (at emission).
The wavelenths are stretched out by the same factor that largescale distances are stretched out during the time the light is in transit.

The standard cosmo model (Friedmann equations) determines a time dependent quantity called the scale-factor a(t). It is an increasing function of time, normalized so that a(now)=1.
Distances between stationary observers increase in proportion to a(t).

The definition of the cosmo redshift z is by this equation:

1+z = a(now)/a(then).

In other words if distances have doubled during the photon's flight, then its wavelength will be stretched out by a factor of 1+z = 2. That is, redshift z=1

If distances have tripled during the photon's flight, then its wavelength will be stretched out by a factor of 1+z = 3. That is, redshift z=2.

These are just conventions, how redshift is defined in relation to the scalefactor a(t).
=========================

a(t) is the basic output of the model (which is derived from the Gen Rel equation, and fits data excellently).
a(t) does not grow at a constant rate. Its growth is determined by the Friedman equation (a specialization of GR).
So the redshift is the cumulative effect of the whole history of the expansion of the universe during the time the photon is in flight and that rate of expansion varies. There is no simple relation between the stretching of wavelength and one or two relative velocities!

Lightwaves are stretched just the same as largescale distances are. By changing geometry. (As distances are between things that are not locked together by physical forces and are free to be at rest relative to the cosmic microwave background.)

Last edited: Jan 16, 2012
5. Jan 17, 2012

### twofish-quant

You can also get 90% of cosmology doing things Newtonian with a bit of SR.

No it isn't. If you have a fixed siren, and you have two objects moving away at the siren at different speeds, you are going to measure different wavelengths. The important thing is the relative speed of the two objects.

This means that wavelength (and hence energy) isn't an intrinsic property of a particle.

6. Jan 17, 2012

### ch@rlatan

I was separating out the 'emission' part of the Doppler effect for demonstration purposes and re-reading my post it seems that I implied that the whole of the Doppler effect occurs at that point. It was unintentional. Thankfully the guy with answers, marcus, read through that.

No. I have to disagree with this. Imagine again the above emission of a photon except at a small enough distance away from the receiving planet so as to have an immeasurably small cosmological red shift. All we are considering then is the Doppler effect. Once away from its emitter the wavelength of the photon is intrinsic. The intrinsicity of wavelength is lost (changed) when the photon is observed (stopped). In an inertial frame of reference that has the emitter as stationary - observers moving toward it note a shorter wavelength (blue shifted) and observers moving away note a longer wavelength (red shifted). In fact, in the case of the Doppler effect alone the intrinsicity of the wavelength can be said to be the wavelength noted by an observer that is stationary with respect to the emitter. Obviously, over vast distances intrinsicity is lost as wavelength is constantly lengthening through the cosmological red shift. But your post was clearly concerned with the Doppler effect and it's that to which I respond.

ch@rlatan.

7. Jan 17, 2012

### ch@rlatan

Good stuff marcus. I'd been convinced by my cosmology textbook that the Doppler effect in light is perfectly analagous to the Doppler effect in sound. So I was relieved when reading your post to see that the intuitive direction I was heading when I asked 'Did the information change en-route?' wasn't too far off the mark. As I understand it now - after doing a little research - cosmological red shift is a function of both the Doppler effect which dominates at shorter distances and concerns simple relative motion (which is why very close galaxies can be blue shifted - and therefore collide) and the expansion of space itself which dominates at longer distances. Cool.

But there is still a question of the mechanism for the information exchange between the 'in transit' photon and the space through which it is transmitted.

I'm not really sure what this means. Can you please elaborate on this?

ch@rlatan.

8. Jan 17, 2012

### Chronos

Bear in mind that expansion increases with cosmological distance. Relative to the star, the planets are receeding at different 'speeds'. Let's say planet A is twice as distant from the star as planet B. This means the recession component of planet A's velocity is twice that of planet B. Now imagine the star is a quarterback, the planets are receivers, and the photons are footballs. The quarterback throws a football to both receivers at the same time at the same velocity. Receiver A is receeding more quickly from the quarterback than receiver B. Which receiver feels more 'sting' upon catching the football?

9. Jan 18, 2012

### litup

Here is my conundrum in regards to redshift: I heard energy cannot be destroyed, only converted. But when the universe expands, it's as if someone is poking new universe space in between the old ones and therefore light goes to a longer wavelength. That says the light now has less energy. Where did the energy it used to have before the expansion expanded 5 billion years ago, where did that energy go?

10. Jan 18, 2012

### Chronos

The quick and dirty answer is energy is not conserved in GR. But, the deeper explanation is [of course] more complicated. There is no unambiguous description of energy in GR, which makes it quite difficult to even entertain the notion of global energy conservation. An analogy [admittedly flawed] of cosmological redshift would be a sine wave drawn on a rubber sheet. If you stretch the rubber sheet in every direction [mimicking expansion of the universe], the sine wave also stretches.

11. Jan 18, 2012

### ch@rlatan

This is the question of energy exchange that I am posing, except you are asking 'where has it gone?' and I am asking 'how was it taken?'.

Logically, if something is acting upon the photon to change it then it must do it by applying a force - in this case it would seem that only a very weak force is needed. Also, that force must act constantly upon the photon throughout its passage in space. If it didn't, the information we infer from redshift data would be compromised.

There is only one 'thing' that constitutes a weak force and which permeates all of space and by deduction it must be the same thing that is acting upon the photon - the cosmic microwave background radiation (CMBR). Does the expansion 'steal' energy from the photon to create space and thus maintain a stable CMBR? There are models, based on laws of thermodynamics, that eventually see a completely cold and empty universe which is consistent with the idea of 'energy theft'. Matter converting to energy and energy converting to space. Maybe it's the very reason for the expansion itself and our notion of cause and effect needs reversing.

The analysis of such an idea is frustrated as we don't know what energy is. Particle / wave duality is a question of form only. We're great at measuring energy and getting it to do the stuff we want it to do but its true nature eludes us and probably always will.

Nevertheless, if you can take Hubble's Law and information about the CMBR then deduce a mathematical proposition based on the idea of energy theft and expansion. Then show that to be consistent with Einstein's highly trusted and predictive General Theory of Relativity. Well, there's a \$1,000,000 prize waiting for you in Switzerland. There's definitely a paper there. Good luck with that.

ch@rlatan.

12. Jan 19, 2012

### Chronos

Are you suggesting dark energy is responsible for cosmological redshift?
My error, you are suggesting refrigerator fairies.
What model do you have in mind? I havent seen one that does not involve fairies
I believe the million is awaiting in Sweden, but, perhaps you have rewritten geography, as well as physics.

13. Jan 19, 2012

### ch@rlatan

I know.....that's what I'm saying??

Not at all. Dark energy is a hypothetical concept - thought by many to be the effect of the cosmological constant and is a measure of what we don't know. On the other hand the CMBR is very real and measurable. What's more it's the same stuff as a photon - electromagnetic radiation.

It's a logical deduction. If it is erroneous in construction then logic can destroy it. I'm always happy to hear your argument.

The cosmological hypothesis called the 'Big Rip'.....and.......I know.......you don't seem to be seeing a lot of things that don't involve them.

:surprised OMG!!!!! You got me!!! I could make the lame excuse that earlier I was looking at the CERN website brushing up on my quantum chromodynamics but....I know....it's unforgivable. I'll be sure to hang up my physics apron.

ch@rlatan.

14. Jan 19, 2012

### Chronos

This is what has me baffled - the CMB is comprised of the most ancient photons in the universe and is afflicted with most severe case of cosmological redshift [z~1100] in the universe, so, how can the CMB be stealing energy from less ancient photons emitted from less distant sources?

15. Jan 19, 2012

### twofish-quant

In that case you have a different wavelength based on different relative motion. You can also have different wavelengths due to gravitation redshift.

Very strongly disagree. Wavelength is like energy or momentum. Different observers can measure different energies and momenta in different reference frames. If you switch reference frames, then of course the wavelength is going to change.

Don't think that's true. Given a photon, the wavelength is going to be different in different reference frames. One thing that you can do is to mark the points at which the wave is at its peak, and then it becomes obvious that different observers are going to see different wavelengths.

16. Jan 19, 2012

### twofish-quant

Think of EM waves as waves. If you think of them as "length of waves" then everything works out. Wavelength changes in different reference frames in exactly the same way that length, time, energy, and momentum changes in different reference frames.

If you are on a beach, and you sail a boat either toward the waves or away from them, the length of the waves change in your new reference frame.

One sign that you've got it wrong is when you have to end up with more and more complex explanations for what is going on. Let's forget about photons for a moment and use the wave picture of EM. We are dealing with microwaves here. You write down electrical and magnetic field strengths and all of those change based on what reference frame you are looking at the problem in.

No there isn't. There is some bookkeeping to make sure that you get consistent results but its something that would make a nice upper level undergraduate or lower graduate level homework problem. One reason that it makes a nice homework problem is that you have get the basic conceptual picture right in order to come up with reasonable answers.

Last edited: Jan 19, 2012
17. Jan 20, 2012

### ch@rlatan

Hey Chronos,

I think the best example to give here is Young's double-slit experiment which provides a clear demonstration of the interference of lightwaves (interference fringes). The age of the light is not a property of it - though time is inferred from its energy. The significant difference in energies (wavelength) of the CMBR and the 'new' light may - and I am not beholden to this notion - constitute a small interference. That interference must mean that both parties have exchanged information (that which we measure as cosmological redshift in the observed light) whilst in contact through the void.

ch@rlatan.

18. Jan 20, 2012

### bapowell

I'm amazed that this thread has carried on as long as it has without someone requesting the OP provide a precise definition of information. Although I think this might be moot at this point...

19. Jan 20, 2012

### Chronos

Photons do not interact with other photons, save under special high energy conditions - and CMB photon energies are much too low for this to occur. This is well explained by QED. So, there is no known mechanism by which CMB photons can 'lose' energy to other photons they encounter during their long journey from the surface of last scattering.

20. Jan 27, 2012

### ch@rlatan

Hey twofish-quant,

General response to your last posts:

Enough with the SR already. You are trying to root this question in SR. It is not a question of observers. A unobserved photon from a distant source passing over our heads and off into the void has still undergone cosmological redshift. The question is 'what mechanism was involved in diminishing that photon's energy?'

As far as the intrinsicity of the photon is concerned, ask yourself this question; 'When distant light-source data is collected - hydrogen line spectra, let's say - to what is it compared in order that its redshift can be determined?'

And your insistence in extrapolating the analogy of the nature of light as a 'wave' is confusing at best, completely wrong at worst.
Planck, through his resolution of the 'ultraviolet catastrope', and Einstein with his Nobel winning paper on the 'photoelectric effect' showed light to be quantized and though the wave theory of light (Huygens'), at that time, was still thought to be wholly descriptive of em-radiation - there was nothing in the wave analogy toolbox that could account for the particle behaviour of light.
The wave theory describes light energy as being continuously absorbed by matter yet the particle (quantum) theory showed conclusively that light is absorbed (and emitted) in discrete packets.
With the discovery of the electron we were able to measure light (energy) to very high degrees by detecting the extent to which the electron is affected by it. But we can only deduce a 'transfer of energy' through the interaction between light and the electron - by detecting the release of energy when the electron returns to its ground state - nothing more. We can not know, through observation, what the energy exchange mechanism is or what light is doing when in transit. We have no medium in which we can resolve (see) light. Our understanding of light can only really be furthered by our understanding of its 'receptor' - the electron. Until we reach that state of knowledge we have to accept - without favouritism - the wave/particle duality of the nature of light.

So we measure light through the quantised interpretation and analyze it in the wave interpretation. It is not possible to observe frequency, and thus wavelength, directly - they are determined by Planck's constant (h) from an observed energy (E). In terms of the particle theory, frequency can be defined as 'how many times light goes through a phase 'cycle' per second' and wavelength can be interpreted as 'the distance that light travels (at c) in completing a single cycle'.

Ahhhh,.............. the old feedback loop.

Okay, let's take a long radio wave.....at the short end of the longwave 'spectrum'....let's say 10^5m or 100 kilometres. So at what point does this wave impart its energy to an electron? You are using wave analogies to explain a wave analogy. Whenever anyone thinks about light (energy), both the wave and particle analogies should be borne in mind - wave/particle duality. If things work with one and not the other there's a problem. Somebody once told me.......

......and never a truer word said.

ch@rlatan

Last edited: Jan 27, 2012